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Francesca Tombari: Vietoris-Rips complexes in TDA and their decompositions

Time: Fri 2019-10-11 13.00 - 14.00

Location: Room 3418, Lindstedtsvägen 25, 4th floor, Department of Mathematics, KTH

Participating: Francesca Tombari

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The aim of topological data analysis (TDA) is to study
datasets using tools from algebraic topology. The step zero in this
process is to put some geometrical structure on the dataset we want to
analyze. Interpreting a dataset as a pseudo-metric space, one can build
the Vietoris-Rips complex, a filtered simplicial complex whose vertices
are the data-points. The goal of this talk will be to familiarize with
Vietoris-Rips complexes, give results about their decompositions from a
homotopical point of view, and see how they are actually direct
consequences of more general statements about simplicial complexes.